Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of
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3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo
Dang Dinh Ang Rudolf Gorenflo Vy Khoi Le Dang Duc Trong
Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction
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Authors Dang Dinh ANG Department of Mathematics and Informatics HoChiMinh City National University 227 Nguyen Van Cu, Q5 Ho Chi Minh City Viet Nam e-mail: [email protected]
Vy Khoi LE Department of Mathematics and Statistics University of Missouri-Rolla Rolla, Missouri 65401 USA e-mail: [email protected]
Rudolf GORENFLO Department of Mathematics and Informatics Free University of Berlin Arnimallee 3 14195 Berlin Germany e-mail: gorenfl[email protected] http://www.fracalmo.org
Dang Duc TRONG Department of Mathematics and Informatics HoChiMinh City National University 227 Nguyen Van Cu, Q5 Ho Chi Minh City Viet Nam e-mail: [email protected]
Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Moment theory and some inverse problems in potential theory and heat conduction / Dang Dinh Ang .... - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in mathematics ; 1792) ISBN 3-540-44006-2
Mathematics Subject Classification (2000): 30E05, 30E10, 31A35, 31B20, 35R25, 35R30, 44A60, 45Q05, 47A52 ISSN 0075-8434 ISBN 3-540-44006-2 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10884684
41/3142/ du - 543210 - Printed on acid-free paper
Foreword In recent decades, the theory of inverse and ill-posed problems has impressively developed into a highly respectable branch of Applied Mathematics and has had stimulating effects on Numerical Analysis, Functional Analysis, Complexity Theory, and other fields. The basic problem is to draw useful information from noise contaminated physical measurements, where in the case of ill-posedness, naive methods of evaluation lead to intolerable amplification of the noise.
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